FIR Filter Coefficient Quantization Calculator
Estimate fixed-point coefficient word-length needed for an FIR filter to meet a given stopband attenuation after quantization.
How to Use
- Enter required stopband attenuation (dB) and filter length N.
- Tool estimates minimum coefficient word-length (bits) to preserve the stopband spec.
Show Work
Formulas
History of Fixed-Point Filter Design
Alan Oppenheim and Ron Schafer's 1975 textbook Digital Signal Processing formalized coefficient-quantization analysis - showing that filter stopband attenuation is limited by ~(6B - 4) dB where B is the coefficient word length. Texas Instruments' TMS32010 (1982, first commercial DSP chip) had 16-bit coefficient storage, limiting filters to ~90 dB stopband. Modern audio DSPs and FPGAs use 18-32 bit coefficients for professional audio applications.
About This Calculator
Enter required stopband attenuation (dB) and FIR filter length (number of taps). The tool estimates minimum coefficient word-length B = (A_s + 4 + 10·log(N))/6 and recommends nearest hardware-friendly word size (16, 18, 24 bits).
For real designs, use Matlab\'s fxpconvert, Python\'s scipy.signal.firwin2 + quantization, or your FPGA vendor\'s filter-synthesis tool. This is a first-pass estimate for specification purposes. Everything runs client-side.
About the FIR Filter Coefficient Quantization Calculator
Whether you are at a desk or on your phone, the FIR Filter Coefficient Quantization Calculator makes electronics and circuit design easy — and it is completely free. Estimate fixed-point coefficient word-length needed for an FIR filter to meet a given stopband attenuation after quantization.
How it works
Type your numbers into the boxes. The answer shows up right away — you do not have to press a button. If you change a number, the answer changes too. So you can try different numbers and watch what happens, or check an answer you worked out yourself. Just make sure each box has the right kind of number in it.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
Why quantize?
Fixed-point DSPs and FPGAs use finite-precision coefficient storage. Rounding off bits distorts the ideal frequency response — especially stopband. More bits = better fidelity but more hardware.
Rule of thumb?
Word length B bits gives ~(6B − 4) dB stopband attenuation limit. For 80 dB: need ≥ 14-bit coefs. For 100 dB: ≥ 18-bit. Adds ~6 dB per extra bit.
Floating point?
Single-precision IEEE 754 gives ~24 mantissa bits → ~140 dB — more than any practical filter needs. Double precision is overkill for DSP. Fixed-point (Q format) wins on power and throughput.
How do I use the FIR Filter Coefficient Quantization Calculator?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Is it free? Does it work without internet?
Yes to both. It is free with no sign-up, and once the page has loaded it keeps working even with no internet.
Where does my data go?
Nowhere — every calculation runs on your own device. Nothing you enter is uploaded, logged, or stored.
Common Use Cases
Audio ADC Decimator
96 dB target: use 18-20 bit coefficients on Q1.17 format.
Software Radio
80 dB adjacent-channel rejection: 16-bit coefs are minimum.
FPGA Implementation
Xilinx DSP48 multiplier: 18×18 bit → 80+ dB filter achievable.
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